The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a standard deviation of $0.20. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs yield a mean cost of $0.95 with a standard deviation of $0.18. Do the data support the claim at the 1% level?

|t| =|-0.96|=0.96< 2.718

since calculated' t' value is less than tabulated value 't'.

we accept null hypothesis at 1 % level of significance.

The data support the claim that the mean cost of a daily news paper is  $1.00

Step-by-step explanation:

Step:-(1)

Given the sample size n = 12

Given Twelve costs yield a mean cost of $0.95 with a standard deviation of $0.18

mean of the sample(x⁻) = $0.95

Standard deviation of sample (S) = $0.18

Given claim that the mean cost of a daily newspaper is $1.00.

The mean of the population 'μ' =  $1.00.

Null hypothesis:-H₀:'μ' =  $1.00.

Alternative hypothesis: H₁:'μ' ≠  $1.00.

level of significance ∝ = 0.01

Step2:-

The test statistic

on calculation, we get

t = -0.96

|t| =|-0.96|=0.96

Degrees of freedom γ = n-1 = 12-1 =11

tₐ =  2.718

Calculated value t = 0.96

Tabulated value t at 0.01 level for 11 degrees for two tailed test = 2.718

since calculated' t' value is less than tabulated value 't'.

conclusion:-

we accept null hypothesis at 1 % level of significance.

The data support the claim that the mean cost of a daily news paper is  $1.00

∞ this is your sign

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1